This mathematics problem involves applying core mathematical principles and formulas. Below you will find a complete step-by-step solution with detailed explanations for each step, helping you understand not just the answer but the method behind it.
ScanSolve AI Answer
To simplify the expression (x^2 - 4x + 4)(x^2 - 4x) + 3, we will expand the product and then combine like terms. Step 1: Let y = x^2 - 4x. Substitute y into the expression. The expression becomes (y + 4)y + 3. Step 2: Expand the expression in terms of y. (y + 4)y + 3 = y^2 + 4y + 3 Step 3: Substitute y = x^2 - 4x back into the expanded expression. (x^2 - 4x)^2 + 4(x^2 - 4x) + 3 Step 4: Expand (x^2 - 4x)^2 using the formula (a-b)^2 = a^2 - 2ab + b^2. Here, a = x^2 and b = 4x. (x^2 - 4x)^2 = (x^2)^2 - 2(x^2)(4x) + (4x)^2 = x^4 - 8x^3 + 16x^2 Step 5: Expand 4(x^2 - 4x). 4(x^2 - 4x) = 4x^2 - 16x Step 6: Combine all the expanded terms. (x^4 - 8x^3 + 16x^2) + (4x^2 - 16x) + 3 Step 7: Combine like terms. x^4 - 8x^3 + (16x^2 + 4x^2) - 16x + 3 x^4 - 8x^3 + 20x^2 - 16x + 3 The simplified expression is: x^4 - 8x^3 + 20x^2 - 16x + 3 Send me the next one 📸